Problem: Simplify the following expression: $ p = \dfrac{-2}{5} - \dfrac{1}{z + 5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{z + 5}{z + 5}$ $ \dfrac{-2}{5} \times \dfrac{z + 5}{z + 5} = \dfrac{-2z - 10}{5z + 25} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{1}{z + 5} \times \dfrac{5}{5} = \dfrac{5}{5z + 25} $ Therefore $ p = \dfrac{-2z - 10}{5z + 25} - \dfrac{5}{5z + 25} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-2z - 10 - 5 }{5z + 25} $ Distribute the negative sign: $p = \dfrac{-2z - 10 - 5}{5z + 25}$ $p = \dfrac{-2z - 15}{5z + 25}$